Question

For the circuit diagram shown, capacitive reactance $X_C=100\Omega ,$ inductive reactance $X_L=200\Omega$ and Resistance $R=100\Omega$. The effective current through the ac source of $200V$ is $\sqrt{N}$, then $N$ is

Answer 1

$KCL\overline{i}=\overline{i_1}+\overline{i_2}$ (Phasor addition)


Since $X_L>X_C,i_2$ will lag the voltage
by $\frac{\pi }{2}.$
$i_1=\frac{V_0}{R}=\frac{200}{100}=2A{i}_2=\frac{V_0}{X_L-X_C}=\frac{200}{200-100}=2A{i}_0=\sqrt{i_1^2+i_2^2}{i}_0=\sqrt{4+4}{i}_0=\sqrt{8}A$